Problem: This is the easy version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.

Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version all prices are different.

An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.

You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.

The second line contains n different integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.

Output

In the first line print the maximum number of ice spheres that Sage can buy.

In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

Example

Input


5
1 2 3 4 5


Output


2
3 1 4 2 5 

Note

In the example it's not possible to place ice spheres in any order so that Sage would buy 3 of them. If the ice spheres are placed like this (3, 1, 4, 2, 5), then Sage will buy two spheres: one for 1 and one for 2, because they are cheap.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.Collections;
public class div2_671_D1 implements Runnable
{
    public void run()
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt();
        int a[] = new int[n];
        for(int i=0;i<n;i++)
        {
            a[i]=sc.nextInt();
        }
        sortintarray.sort(a);
        if((n&1)==0)
        {
            System.out.println((n/2)-1);
        }
        else
        {
            System.out.println(n/2);
        }
        
        int l=0,r=n-1;
        while(l<=r)
        {
            if(l==r)
            {
                System.out.print(a[l]);
                l++;
                r--;
            }
            else
            {
                System.out.print(a[r]+" "+a[l]+" ");
                l++;
                r--;
            }
        }
    }

    static class sortintarray {
        public static void sort(int[] arr) {
            int n = arr.length, mid, h, s, l, i, j, k;
            int[] res = new int[n];
            n--;
            for (s = 1; s <= n; s <<= 1) {
                for (l = 0; l < n; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n);
                    mid = Math.min(l + s - 1, n);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h) res[k++] = (arr[i] <= arr[j] ? arr[i++] : arr[j++]);
                    while (i <= mid) res[k++] = arr[i++];
                    while (j <= h) res[k++] = arr[j++];
                    for (k = l; k <= h; k++) arr[k] = res[k];
                }
            }

        }
    }

    static class sortchararray {
        public static void sort(char[] arr) {
            int n = arr.length, mid, h, s, l, i, j, k;
            char[] res = new char[n];
            n--;
            for (s = 1; s <= n; s <<= 1) {
                for (l = 0; l < n; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n);
                    mid = Math.min(l + s - 1, n);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h) res[k++] = (arr[i] <= arr[j] ? arr[i++] : arr[j++]);
                    while (i <= mid) res[k++] = arr[i++];
                    while (j <= h) res[k++] = arr[j++];
                    for (k = l; k <= h; k++) arr[k] = res[k];
                }
            }
        }
    }

    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}

    long factorial(long n){    
      if (n == 0)    
        return 1;    
      else    
        return(n * factorial(n-1));    
    }

    boolean isPrime(int n) 
    {
        if (n <= 1){
            return false;
        }

        for (int i = 2; i < n; i++){
            if (n % i == 0){
                return false; 
            }
      
        }  
        return true; 
    }

    long ceil(long a,long b)
    {
        if(a%b==0)
        {
            return a/b;
        }
        else
        {
            return (a/b)+1;
        }
    }
    int ceil(int a,int b)
    {
        if(a%b==0)
        {
            return a/b;
        }
        else
        {
            return (a/b)+1;
        }
    }

    public static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
        public U x;
        public V y;
    
        public Pair(U x, V y) {
            this.x = x;
            this.y = y;
        }
    
        public int hashCode() {
            return (x == null ? 0 : x.hashCode() * 31) + (y == null ? 0 : y.hashCode());
        }
    
        public boolean equals(Object o) {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            Pair<U, V> p = (Pair<U, V>) o;
            return (x == null ? p.x == null : x.equals(p.x)) && (y == null ? p.y == null : y.equals(p.y));
        }
    
        public int compareTo(Pair<U, V> b) {
            int cmpU = x.compareTo(b.x);
            return cmpU != 0 ? cmpU : y.compareTo(b.y);
        }
    
        public String toString() {
            return String.format("(%s, %s)", x.toString(), y.toString());
        }
    
    }   

    static class InputReader 
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
       
        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();
           
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
               
                if(numChars <= 0)              
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();
           
            while(isSpaceChar(c))
                c = read();
           
            int sgn = 1;
           
            if (c == '-') {
                sgn = -1;
                c = read();
            }
           
            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
           
            return res * sgn;
        }
       
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
           
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
       
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
       
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));
           
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() {
            return readString();
        }
       
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new div2_671_D1(),"Main",1<<27).start();
    }
}